Did Prophet(pbuh) chose someone as Caliph !

bro, first of all the ayats you have mentioned about Islam overcoming all the other religions refer to the time of the return of Imam Mahdi and Hazrat Isa (as). This will be the time when Islam and its teachings will overcome other religions and Quran o Sharia will be the basis of the rule all over the world. This is much more logical and understandable understanding of the ayats you mentioned because its been 1400+ years since the message of Islam has completed, and anybody with fair mind could see that Islamic ummat is at the moment playing hardly any role as far as prevailing teachings such as justice, fairplay, human rights, brotherhood, racism, tribal/caste systems, women rights etc are concerned.

Islamic teachings no doubt proclaim and exceed other religions and ideas of this world. However we must ponder hard why we as Muslims have lagged behind from the other nations.

Secondly, the khutba of Imam Ali 126 from Nahjul Balagha, the people of extremes are those who said he was God (Alawis, Nussayria), and the other extreme was those who hated him to death (Khawarijias, Nasibis, Muawiyya supporters etc). The middle majority were the Muslims, which included both the shias and the sunnis (check the context and the occassion this khutba was given from both Shia and Sunni sources that commented on Najul Balagha).

Now as for the hadiths stating that majority sect will be right etc, there are numerous questions that require answer. First of all which one is the majority sect? I think if you go by commonly published statistics it is Hanafis who make between 300 to 400 million. And then Jaafaris who make between 250 and 300 million and so on.
And if any of us think that all the Shias or Sunnis or subgroups such as 12ers or Malikies were to go to jannat judged upon the sectarian tags they were born with, then i believe it to be seriously flawed way of thinking that directly challenges Allahs' justice system. This also contradicts the principles stated in the Holy Quran, such as when Quran states:

5:69 for, verily, those who have attained to faith [in this divine writ], as well as those who follow the Jewish faith, and the sabians, and the Christians - all who believe in God and the Last Day and do righteous deeds - no fear need they have, and neither shall they grieve.

There are plenty more ayats like this in praise of "righteous" Christians, Jews etc. Bro, only the people with good aamals will go to Jannat OR the people who are lucky enough to get Shifaa't from the special loved ones of Allah as stated in the Quran, Allahu Aalam.

Looking towards majority in search of 'haq' is a weak arguments for one that has no basis in the Quran o Sunnat whatsoever. Therefore i doubt the above hadiths to be true, AllahuAlam.

Lastly bro, my views again differ from you as far as the question of who has sacrificed most for Islam is concerned. There has been noone who could claim to have saved Islam other than the Aaema (as). Their sacrifices and educationals services are surely unmatchable. At the same time both sincere Shia and Sunni people have given their soul and blood for the religion too during different periods in time. I am proud to say at the moment Sunni Hamas is bring supported by Shia Iran, Hezbollah, Syria block because Hamas are simply with haq. This is the attitude that we all must develop if we are to progress.

Last but not least i agree with you for once where u have quoted Umar as saying:

"someone better than me [abu bakr] choose one but someone better than him i.e Prophet] did not so I will not choose one"

I agree that Abu Bakr was not chosen by the Prophet (saww) just as stated in the quote above.

Insha Allah i pray to Allah to keep us all on the right path, and give us strength and capability to learn more by every passing day.